Stocks and other securities and financial instruments are frequently arranged in portfolios or other collections containing numerous different financial assets. A problem in portfolio management is understanding the co-movement of different assets or asset classes, and the implications for portfolio construction and risk management. According to one embodiment, co-movement is the correlation of asset prices or valuations over time (for example, which stocks tend to rise or drop in value as a group). Diversifying such portfolios (such as including assets whose financial behavior tends to be independent over time as opposed to being highly correlated) is one of several important financial investment functions.
Analyzing the correlation of a small number (such as six or fewer) of different stocks may be relatively straightforward. For example, one may directly examine the matrix of correlations or co-movement indicators (i.e., an N×N matrix for N assets) since such a matrix has relatively few distinct entries (at most a few dozen for N≤6). However, when analyzing a large number of assets (for example, 100 or 500 such assets), the number of combinations of any two of them grows quadratically and quickly overwhelms any attempt by an investor to grasp the structure of the correlation matrix as a whole, or to derive salient characteristics from it for investment purposes.